Question

Find the largest positive integer that will divide 100 245 and 343 leaving remainder 4 5 7 respectively

Answer 1

Answer:

48

Step-by-step explanation:

Leaving a remainder of 4 when dividing into 100 means the number must divide 96.

Leaving a remainder of 5 when dividing into 245 means it divides 240.

Leaving a remainder of 7 when dividing into 343 means it divides 336.

What we want then is the HCF of the numbers 96, 240, 336.  This is easily found from prime factorizations.

96 = 2⁵ × 3

240 = 2⁴ × 3 × 5

336 = 2⁴ × 3 × 7

So the HCF is 2⁴ × 3 = 48.

Answer 2

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